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Wiktor Eckhaus
Wiktor Eckhaus (28 June 1930 – 1 October 2000) was a Polish–Dutch mathematician, known for his work on the field of differential equations. He was Professor Emeritus of Applied Mathematics at the Utrecht University. Biography Eckhaus was born into a wealthy family, and raised in Warsaw where his father was managing a fur company. During the German occupation of Poland, he, his mother and sister had to hide because of their Jewish descent. His father, after being a prisoner of war, joined the Russian Army. After the war, in 1947, the re-united family came to Amsterdam – via a refugee camp in Austria. Wiktor passed the state exam of the Hogere Burgerschool in 1948, and started to study aeronautics at the Delft University of Technology. Following his graduation he worked with the National Aerospace Laboratory in Amsterdam, from 1953 till 1957. In the period 1957–1960 he worked at the Massachusetts Institute of Technology, where Eckhaus earned a PhD in 1959 under Leon Trilli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iwano-Frankiwsk
Ivano-Frankivsk ( uk, Іва́но-Франкі́вськ, translit=Iváno-Frankívśk ), formerly Stanyslaviv ( pl, Stanisławów ; german: Stanislau), is a city located in West Ukraine, Western Ukraine. It is the administrative centre of Ivano-Frankivsk Oblast and Ivano-Frankivsk Raion. Ivano-Frankivsk hosts the administration of Ivano-Frankivsk urban hromada. Its population is Built in the mid-17th century as a fortress of the Polish Potocki family, Stanisławów was annexed to the Habsburg monarchy, Habsburg Empire during the First Partition of Poland in 1772, after which it became the property of the State within the Austrian Empire. The fortress was slowly transformed into one of the most prominent cities at the foothills of the Carpathian Mountains. After World War I, for several months, it served as a temporary capital of the West Ukrainian People's Republic. Following the Peace of Riga in 1921, Stanisławów became part of the Second Polish Republic. After the Soviet in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warsaw
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officially estimated at 1.86 million residents within a greater metropolitan area of 3.1 million residents, which makes Warsaw the 7th most-populous city in the European Union. The city area measures and comprises 18 districts, while the metropolitan area covers . Warsaw is an Alpha global city, a major cultural, political and economic hub, and the country's seat of government. Warsaw traces its origins to a small fishing town in Masovia. The city rose to prominence in the late 16th century, when Sigismund III decided to move the Polish capital and his royal court from Kraków. Warsaw served as the de facto capital of the Polish–Lithuanian Commonwealth until 1795, and subsequently as the seat of Napoleon's Duchy of Warsaw. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular Perturbation Theory
In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uniformly approximated by an asymptotic expansion :\varphi(x) \approx \sum_^N \delta_n(\varepsilon) \psi_n(x) \, as \varepsilon \to 0. Here \varepsilon is the small parameter of the problem and \delta_n(\varepsilon) are a sequence of functions of \varepsilon of increasing order, such as \delta_n(\varepsilon) = \varepsilon^n. This is in contrast to regular perturbation problems, for which a uniform approximation of this form can be obtained. Singularly perturbed problems are generally characterized by dynamics operating on multiple scales. Several classes of singular perturbations are outlined below. The term "singular perturbation" was coined in the 1940s by Kurt Otto Friedrichs and Wolfgang R. Wasow. Methods of analysis A perturbed problem whose solution can be approximated on the wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh–Bénard Convection
In fluid thermodynamics, Rayleigh–Bénard convection is a type of natural convection, occurring in a planar horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as Bénard cells. Bénard–Rayleigh convection is one of the most commonly studied convection phenomena because of its analytical and experimental accessibility. The convection patterns are the most carefully examined example of self-organizing nonlinear systems. Buoyancy, and hence gravity, are responsible for the appearance of convection cells. The initial movement is the upwelling of less-dense fluid from the warmer bottom layer. This upwelling spontaneously organizes into a regular pattern of cells. Physical processes The features of Bénard convection can be obtained by a simple experiment first conducted by Henri Bénard, a French physicist, in 1900. Development of convection The experimental set-up uses a layer of liquid, e.g. water, between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrodynamic Stability
In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these instabilities will cause the development of turbulence.See Drazin (2002), ''Introduction to hydrodynamic stability'' The foundations of hydrodynamic stability, both theoretical and experimental, were laid most notably by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century. These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations, and the Navier–Stokes equations. When studying flow stability it is useful to understand more simplistic systems, e.g. incompressible and inviscid fluids which can then be developed further onto more complex flows. Since the 1980s, more computational methods are being used to model and analyse the more complex flows. Stable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Airfoil
An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turbine. A solid body moving through a fluid produces an aerodynamic force. The component of this force perpendicular to the relative freestream velocity is called lift. The component parallel to the relative freestream velocity is called drag. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. Airfoils can be designed for use at different speeds by modifying their geometry: those for subsonic flight generally have a rounded leading edge, while those designed for supersonic flight tend to be slimmer with a sharp leading edge. All have a sharp trailing edge. Foils of similar function designed with water as the working fluid are called hydrofoils. The lift on an airfoil is primarily the result o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Flow
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Centre
The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Council (NWO) and is located at the Amsterdam Science Park. This institute is famous as the creation site of the programming language Python (programming language), Python. It was a founding member of the European Research Consortium for Informatics and Mathematics (ERCIM). Early history The institute was founded in 1946 by Johannes van der Corput, David van Dantzig, Jurjen Koksma, Hendrik Anthony Kramers, Marcel Minnaert and Jan Arnoldus Schouten. It was originally called ''Mathematical Centre'' (in Dutch: ''Mathematisch Centrum''). One early mission was to develop mathematical prediction models to assist large Dutch engineering projects, such as the Delta Works. During this early period, the Mathematics Institute also helped with designing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Amsterdam
The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being the Vrije Universiteit Amsterdam (VU). Established in 1632 by municipal authorities and later renamed for the city of Amsterdam, the University of Amsterdam is the third-oldest university in the Netherlands. It is one of the largest research universities in Europe with 31,186 students, 4,794 staff, 1,340 PhD students and an annual budget of €600 million. It is the largest university in the Netherlands by enrollment. The main campus is located in central Amsterdam, with a few faculties located in adjacent boroughs. The university is organised into seven faculties: Humanities, Social and Behavioural Sciences, Economics and Business, Science, Law, Medicine, Dentistry. The University of Amsterdam has produced six Nobel Laureates and fiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris
, image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and anywhere on Earth , established = Founded: c. 1150Suppressed: 1793Faculties reestablished: 1806University reestablished: 1896Divided: 1970 , type = Corporative then public university , city = Paris , country = France , campus = Urban The University of Paris (french: link=no, Université de Paris), metonymically known as the Sorbonne (), was the leading university in Paris, France, active from 1150 to 1970, with the exception between 1793 and 1806 under the French Revolution. Emerging around 1150 as a corporation associated with the cathedral school of Notre Dame de Paris, it was considered the second-oldest university in Europe. Haskins, C. H.: ''The Rise of Universities'', Henry Holt and Company, 1923, p. 292. Officially chartered i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
